Sentence examples for bound can be expressed from inspiring English sources

The bound can be expressed in terms of the third non-absolute central moment and a finite sum (see Additional file 2).

With respect to the empirical bound proposed in (Milo et al., 2003) (i.e. N ′ = 100 | E | ), our bound can be expressed as (2) N = N ′ 200 (1 − d ) ln ⁡ (1 − d ) N ′ 100 at least for bipartite graphs.

So, the lower-bound can be expressed as begin{aligned} P_{out,low} &= Pleft(minleftlbrace X_{1},gamma_{RD}rightrbrace leq gamma_{th} right) &=1 - Pleft(minleftlbrace X_{1},gamma_{RD}rightrbrace > gamma_{th} right) &= 1 - bar{F}_{X_{1}}left(gamma_{th} right) bar{F}_{gamma_{RD}}left(gamma_{th} right) end{aligned} (36).

This bound can be derived recursively by simply expressing M X ̂ ( i ) in terms of new observation and an additional regressor X ̂ a ( i ) as follows: M X ̂ ( i ) = min h ∥ h ∥ R h − 1 2 + ∥ Y ( i ) − ρ X ̂ a ( i ) h ∥ 2 = min h ∥ h ∥ R h − 1 2 + Y ( i − 1 ) Y ( i ) − ρ X ̂ a ( i − 1 ) X ̂ a ( i ) h 2 (19).

From Theorem 5 and substituting p using (3), the lower bound L A can be expressed as L A = log 2 S c ; if Ω c ≥ log 2 S c − 2 log 2 S c − 1 + 1, log 2 S c + 1 ; otherwise.

From (23) and (34), the lower bound of ECOMF multicast rate can be expressed as (35).

The cut-set upper bound for the considered relay network can be expressed as [14] R ( cut - set b. ) = max { λ ¯, λ i, λ i ¯, λ } ≥ 0 R (20a).

Upper bound, lower bound, and central values for failure rates and repair rate can be expressed through triangular fuzzy numbers.

The uncertainty of the estimated parameters at each voxel can be expressed by the Cramér Rao lower bound (CRLB), which gives a lower bound for the variance [ 12– 12].

By replacing the original cost function in (13) with its lower bound (16), the modified joint power allocation problem can be expressed as (17).

By taking the minimum upper bound for each case, the sum-capacity C DDF can be expressed as Fig. 5 The achievable rate regions and sum-capacities of DDF relaying mode for different interferences cases.